Ah. So this is a serious, "pay me" sort of endeavor. I was thinking perhaps you might do it just out of love with hopes of a possible publication.
In that case, definitely go with a teleplay. Obviously, if you're looking to get paid, a screenplay would not stand a chance at getting picked up. Star Trek has officially been relaunched on the big screen with the upcoming movie. From what I know of you, your screenplay would not fit into that established universe at all and would therefore be disregarded. A good teleplay, on the other hand, could be picked up by Cawley and company or even by a network.
I would also suggest going all the way back to the days of April just to add more seperation between your story and the film's story.